Dalek Thay is one of the four members of the Cult of Skaro. Along with the other cult members, he fled the Time War by escaping into the Void, eventually reaching 21st century Earth through a breach in the dimensional barriers. When the Cult emerged from their Void sphere, they found themselves inside the headquarters of the Torchwood Institute, a secret organisation dedicated to defending Earth from alien threats. After extracting the brainwaves of a Torchwood scientist, the Cult learned of an invasion in-progress by another extra-terrestrial force.
Dalek Sec ordered Dalek Thay to investigate the area. As Thay explored the Torchwood Tower, he encountered two of the invaders: Cybermen. Sec and the other cultists watched via a comm window as Thay and the Cybermen identified each other and the Cybermen extended an offer of an alliance between them and the Daleks. Thay denied the request and the Cybermen took the refusal as an act of hostile intent, opening fire with their blasters. The shots were absorbed by Thay's shields, who then retaliated by shooting the two Cybermen dead with his energy weapon. Thus the Daleks declared war against the Cybermen.
Dalek Thay took part in The Battle of Canary Wharf along with the countless Daleks released from the Genesis Ark, but the slaughter was cut short by the Doctor. He reversed the Void rift that allowed both the Cybermen and Daleks to invade, and so the two armies - saturated in Void particles - were sucked back through and into the oblivion of the Void. The Cult of Skaro - Thay included - survived by using their emergency temporal shift to jump back in time to 1930.
Arriving in New York during the Great Depression, the Cult established a laboratory beneath the city streets where they worked toward the restoration of the Dalek race. Using their human intermediary Diagoras to acquire labourers, the Cult took over construction of the Empire State Building. They added the building's mast to the blueprints, intending to use it as a conductor when a solar flare would trigger a lightning strike. Dalek Thay made a significant contribution to the project by having pieces of his casing removed to make the conductor. The Dalekanium alloy would conduct the gamma radiation from the storm and infuse it into the Cult's army of Dalek-Human soldiers. With pieces of his armour missing, Thay patched up his shell with layers of sheet metal.
Both Thay and Dalek Jast led the Dalek-Humans into an empty theater as they hunted down the Doctor. After exterminating their former leader Dalek Sec, Thay and Jast ordered the Dalek-Humans to kill the Doctor, but the hybrids refused to follow orders because their genes had been infused with Time Lord DNA when the Doctor got in the way of the gamma strike. The hybrids rebelled against their creators and Dalek Thay was destroyed in a barrage of blaster fire.